Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large mixing bowl, combine the all-purpose flour, granulated sugar, baking powder, and salt. Mix well. Add the softened butter, 1 cup of milk, eggs, and 1 teaspoon of vanilla extract. Beat for about 2 minutes until smooth.
Gently fold in the chopped strawberries. Pour half of the batter into the prepared baking dish, sprinkle half of the brown sugar and cinnamon mixture, then pour the remaining batter and top with the rest of the brown sugar mixture.
Bake for 30-35 minutes, checking for doneness with a toothpick.
While the cake is baking, whisk together the powdered sugar, 2 tablespoons of milk, and 1 teaspoon of vanilla extract until smooth for the icing.
Let the cake cool for about 10 minutes, then drizzle the icing over the warm cake.